On the integral Hodge conjecture for real abelian threefolds

Abstract We prove the real integral Hodge conjecture for several classes of real abelian threefolds. For instance, we prove the property for real abelian threefolds whose real locus is connected, and for real abelian threefolds A which are the product A = B × E {A=B\times E} of an abelian surface B and an elliptic curve E with connected real locus E ⁢ ( ℝ ) {E(\mathbb{R})} . Moreover, we show that every real abelian threefold satisfies the real integral Hodge conjecture modulo torsion, and reduce the principally polarized case to the Jacobian case.